The potential function network addresses the `where to look?' problem for an unseen goal object \(o\) . It uses the semantic map \(m_t\)  and the goal object \(o\)  to predict two potential functions that provide complementary information for ObjectNav (see fig:approach, center). The area potential function \(U_t^a\)  serves as a guide for efficient exploration, and helps find unexplored areas in the environment. Analogous to exploration rewards in RL [1]}, [2]}, it provides a useful exploration bias for ObjectNav. When the semantic map is not informative (for example, at the start of the episode), \(U_t^a\)  is critical to quickly explore and gather information from the environment. The object potential function \(U_t^o\)  serves as a guide for efficient object search (reminiscent of the heuristic in A* search [3]}), and helps find the object \(o\) . When the semantic map is sufficiently informative, \(U_t^o\)  is critical to perform semantic reasoning and quickly find the object. The potential function network combines these potential functions to sample the long-term goal, effectively trading-off between exploring the environment and finding the object.
